# part C, seed 1017, 2026-10-17 06:59
C0 product metric = sum of tree metrics (BFS check on a 70-vertex product): True
C1 Lemma 5 strip walk: 4 x 3000 random/adversarial instances, bound c_d (n^(1-1/d)+1) L never violated; max length/bound by d: {1: 0.4993, 2: 0.2895, 3: 0.1436, 4: 0.0709}
NC_C1 bad-order walk length 798.0 > bound 168.0: True (expected True); strip walk on the same points: 2.0 <= bound: True
C2 random instances: 2100 triples (d = 2, 3, 4; random, regular-ball, spider, path factors); every link of the chain of (i) holds; max (TS+N)^a/(TP+N) = 0.5000 (allowed up to 1/C_d = 4c_d+1 >= 33); max TS/(N^(1-1/d) sigma) = 1.7857
C4 T x K2 remark: TS <= 3 TP + 2 on 200 random triples (max TS - 3TP = 0)
C3 hill-climb [P25xP25] N=6, 600 steps, objective ratio_TS: best 1.0206 (TS=35, sigma=14, N=6)
C3 hill-climb [P25xP25] N=6, 600 steps, objective ratio_final: best 0.3409 (TS=37, sigma=15, N=6)
C3 hill-climb [P25xP25] N=9, 600 steps, objective ratio_TS: best 0.9020 (TS=92, sigma=34, N=9)
C3 hill-climb [P25xP25] N=9, 600 steps, objective ratio_final: best 0.3369 (TS=54, sigma=19, N=9)
C3 hill-climb [T3-ball x T3-ball] N=6, 600 steps, objective ratio_TS: best 0.9526 (TS=28, sigma=12, N=6)
C3 hill-climb [T3-ball x T3-ball] N=6, 600 steps, objective ratio_final: best 0.3524 (TS=25, sigma=11, N=6)
C3 hill-climb [T3-ball x T3-ball] N=9, 600 steps, objective ratio_TS: best 0.8889 (TS=32, sigma=12, N=9)
C3 hill-climb [T3-ball x T3-ball] N=9, 600 steps, objective ratio_final: best 0.3710 (TS=30, sigma=11, N=9)
C3 hill-climb [rrt40 x rrt40] N=6, 600 steps, objective ratio_TS: best 0.9254 (TS=34, sigma=15, N=6)
C3 hill-climb [rrt40 x rrt40] N=6, 600 steps, objective ratio_final: best 0.3877 (TS=26, sigma=10, N=6)
C3 hill-climb [rrt40 x rrt40] N=9, 600 steps, objective ratio_TS: best 0.8718 (TS=34, sigma=13, N=9)
C3 hill-climb [rrt40 x rrt40] N=9, 600 steps, objective ratio_final: best 0.3507 (TS=34, sigma=13, N=9)
C3 hill-climb [P9^3] N=8, 500 steps, objective ratio_TS: best 0.8158 (TS=62, sigma=19, N=8)
NC_C exponent test d=2: (log2 n, ratio at alpha0, ratio at alpha0+0.05) = [(2, 3.567, 2.872523), (5, 4.779, 2.837393), (10, 4.9928, 1.765152), (20, 5.0, 0.624999), (30, 5.0, 0.220971)]; ratio at alpha0+0.05 -> 0 (detected=True), at alpha0 bounded below (min 3.567)
NC_C exponent test d=3: (log2 n, ratio at alpha0, ratio at alpha0+0.05) = [(2, 5.3509, 3.774992), (5, 6.8086, 2.862543), (10, 6.9941, 1.2364), (20, 7.0, 0.21875), (30, 7.0, 0.03867)]; ratio at alpha0+0.05 -> 0 (detected=True), at alpha0 bounded below (min 5.3509)
NC_C wrong sigma (true-1) detected by the independent recount in 300/300 instances
NC_C2 shuffled Euler tour: chain assertion failed in 300/300 instances (must be > 0)
# done in 7.6 s
